Congruence properties of lattices of quasivarieties

K. V. Adaricheva, V. A. Gorbunov, W. Dziobiak

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The congruence properties close to being lower boundedness in the sense of McKenzie are treated. In particular, the affirmative answer is obtained to a known question as to whether finite lattices of quasivarieties are lower bounded in the case where quasivarieties are congruence-Noetherian and locally finite. Namely, we state that for every congruence-Noetherian or finitely generated locally finite quasivariety K, the lattice Lq(K) possesses the Day-Pudlak-Tuma property. But if a quasivariety is locally finite (without the condition of being finitely generated), that lattice satisfies only the Pudlak-Tu̇ma property.

Original languageEnglish
Pages (from-to)349-358
Number of pages10
JournalAlgebra and Logic
Volume36
Issue number6
DOIs
Publication statusPublished - Jan 1 1997

ASJC Scopus subject areas

  • Analysis
  • Logic

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    Adaricheva, K. V., Gorbunov, V. A., & Dziobiak, W. (1997). Congruence properties of lattices of quasivarieties. Algebra and Logic, 36(6), 349-358. https://doi.org/10.1007/BF02671552